Context. Rich globular cluster systems, particularly the metal-poor part of them, are thought to be the visible manifestations of longterm accretion processes. The invisible part is the dark matter halo, which may show some correspondence to the globular cluster system. It is therefore interesting to investigate the globular cluster systems of isolated elliptical galaxies, which supposedly have not experienced extended accretion. Aims. We investigate the globular cluster system of the isolated elliptical NGC 7796, present new photometry of the galaxy, and use published kinematical data to constrain the dark matter content. Methods. Deep images in B and R, obtained with the VIsible MultiObject Spectrograph (VIMOS) at the VLT, form the data base. We performed photometry with DAOPHOT and constructed a spherical photometric model. We present isotropic and anisotropic Jeans-models and give a morphological description of the companion dwarf galaxy. Results. The globular cluster system has about 2000 members, so it is not as rich as those of giant ellipticals in galaxy clusters with a comparable stellar mass, but richer than many cluster systems of other isolated ellipticals. The colour distribution of globular clusters is bimodal, which does not necessarily mean a metallicity bimodality. The kinematic literature data are somewhat inconclusive. The velocity dispersion in the inner parts can be reproduced without dark matter under isotropy. Radially anisotropic models need a low stellar mass-to-light ratio, which would contrast with the old age of the galaxy. A MONDian model is supported by X-ray analysis and previous dynamical modelling, but better data are necessary for a confirmation. The dwarf companion galaxy NGC 7796-1 exhibits tidal tails, multiple nuclei, and very boxy isophotes. Conclusions. NGC 7796 is an old, massive isolated elliptical galaxy with no indications of later major star formation events as seen frequently in other isolated ellipticals. Its relatively rich globular cluster system shows that isolation does not always mean a poor cluster system. The properties of the dwarf companion might indicate a dwarf-dwarf merger.